 9.1.1: Plot the point whose rectangular coordinates are 13, 12. What quad...
 9.1.2: To complete the square of x2 + 6x, add . (pp. A28A29)
 9.1.3: If P = 1a, b2 is a point on the terminal side of the angle u at a d...
 9.1.4: tan1 1 12 = . (pp. 447449)
 9.1.5: The origin in rectangular coordinates coincides with the in polar c...
 9.1.6: True or False In the polar coordinates (r, u), r can be negative.
 9.1.7: True or False The polar coordinates of a point are unique.
 9.1.8: If P is a point with polar coordinates (r, u), the rectangular coor...
 9.1.9: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.10: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.11: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.12: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.13: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.14: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.15: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.16: In 916, match each point in polar coordinates with either A, B, C, ...
 9.1.17: In 1730, plot each point given in polar coordinates
 9.1.18: In 1730, plot each point given in polar coordinates
 9.1.19: In 1730, plot each point given in polar coordinates
 9.1.20: In 1730, plot each point given in polar coordinates
 9.1.21: In 1730, plot each point given in polar coordinates
 9.1.22: In 1730, plot each point given in polar coordinates
 9.1.23: In 1730, plot each point given in polar coordinates
 9.1.24: In 1730, plot each point given in polar coordinates
 9.1.25: In 1730, plot each point given in polar coordinates
 9.1.26: In 1730, plot each point given in polar coordinates
 9.1.27: In 1730, plot each point given in polar coordinates
 9.1.28: In 1730, plot each point given in polar coordinates
 9.1.29: In 1730, plot each point given in polar coordinates
 9.1.30: In 1730, plot each point given in polar coordinates
 9.1.31: In 3138, plot each point given in polar coordinates, and find other...
 9.1.32: In 3138, plot each point given in polar coordinates, and find other...
 9.1.33: In 3138, plot each point given in polar coordinates, and find other...
 9.1.34: In 3138, plot each point given in polar coordinates, and find other...
 9.1.35: In 3138, plot each point given in polar coordinates, and find other...
 9.1.36: In 3138, plot each point given in polar coordinates, and find other...
 9.1.37: In 3138, plot each point given in polar coordinates, and find other...
 9.1.38: In 3138, plot each point given in polar coordinates, and find other...
 9.1.39: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.40: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.41: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.42: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.43: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.44: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.45: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.46: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.47: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.48: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.49: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.50: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.51: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.52: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.53: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.54: In 3954, the polar coordinates of a point are given. Find the recta...
 9.1.55: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.56: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.57: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.58: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.59: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.60: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.61: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.62: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.63: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.64: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.65: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.66: In 5566, the rectangular coordinates of a point are given. Find pol...
 9.1.67: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.68: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.69: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.70: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.71: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.72: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.73: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.74: In 6774, the letters x and y represent rectangular coordinates. Wri...
 9.1.75: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.76: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.77: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.78: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.79: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.80: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.81: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.82: In 7582, the letters r and u represent polar coordinates. Write eac...
 9.1.83: In Chicago, the road system is set up like a Cartesian plane, where...
 9.1.84: Show that the formula for the distance d between two points P1 = 1r...
 9.1.85: In converting from polar coordinates to rectangular coordinates, wh...
 9.1.86: Explain how you proceed to convert from rectangular coordinates to ...
 9.1.87: Explain how you proceed to convert from rectangular coordinates to ...
Solutions for Chapter 9.1: Polar Coordinates
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 9.1: Polar Coordinates
Get Full SolutionsSince 87 problems in chapter 9.1: Polar Coordinates have been answered, more than 77742 students have viewed full stepbystep solutions from this chapter. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.1: Polar Coordinates includes 87 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Column space C (A) =
space of all combinations of the columns of A.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.